A proof-of-concept for automated AI-driven stellarator coil optimization with in-the-loop finite-element calculations

Stage-one stellarator design searches a high-dimensional family of three-dimensional plasma boundaries and fixed-boundary MHD equilibria for configurations that jointly meet requirements on confinement, field-line topology, force balance, stability proxies, and geometry. These specifications do not provide a general constructive map to a validated finite-beta equilibrium. High-quality targets are commonly developed through iterative numerical optimization whose outcome depends on the initial configuration, active Fourier resolution, objective priorities, and local solver budget. Coordinating this process is computationally costly and expert-intensive, limiting both design throughput and the production of consistently evaluated data. We present a proof of concept for agentic stage-one optimization. A bounded language-model agent diagnoses the current equilibrium and selects the next local optimization experiment, while deterministic DESC execution owns prescribed profiles and flux, symmetry, metric evaluation, solver validity, and acceptance. On a common-budget subset from an expanding finite-beta campaign, the number of gate-valid configurations increases from five inputs to nineteen outputs; median Boozer QS RMS decreases from $2.39\times10^{-4}$ to $1.07\times10^{-4}$, and median maximum principal curvature decreases from $62.56$ to $33.00\,\mathrm{m}^{-1}$. A complementary long route achieves a $9.10\times$ QS reduction while repairing magnetic-well and curvature defects. The system also records every attempted local action as transition evidence, yielding 734 structured parent--action--outcome records in the reported experiments. These results show that agentic outer-loop control can sustain finite-beta, multi-objective search and turn repeated optimization into a scalable source of improved equilibria and reusable decision data.

This work evaluates surrogate-assisted optimization of a seven-parameter current-excited coil--core benchmark subject to geometric, manufacturing, and separate core and copper mass constraints. A Python--MPh--COMSOL workflow couples a two-dimensional axisymmetric finite-element method (FEM) model to a Matern 5/2 Gaussian-process (GP) probabilistic surrogate. Here, physics-constrained denotes a design problem evaluated by a governing-equation FEM model and restricted by explicit physical, geometric, manufacturing, and material-allocation constraints; it does not denote a physics-informed GP architecture. Sequential Bayesian optimization (BO) ranks candidates using expected improvement (EI), and every reported incumbent is verified by FEM. Five paired runs show that optimizer ranking depends on the available FEM-evaluation budget: EI--BO improves rapidly at small continuation budgets, COBYLA is stronger at the earliest checkpoint, and BOBYQA attains the highest mean terminal response. A retrospective finite-pool study further finds no robust endpoint advantage of EI over posterior-mean ranking on this smooth response surface. The broader result is that early progress, terminal response, information use, and wall-clock cost can favor different methods in simulation-driven design. A selected-design check at a common total current preserves the observed BOBYQA--COBYLA--EI-BO ordering. The conclusions nevertheless remain conditional on this axisymmetric benchmark and do not establish a fixed-current optimum, fixed-power performance, or electrical-efficiency superiority.

Agentic AI has automated parts of scientific discovery, including paper generation, expert-level coding, therapeutic proposal, and autonomous experimentation. Complex physical engineering design remains a gap, because candidates must satisfy simultaneous constraints in fluid dynamics, solid mechanics, and structural stability. We introduce The AI Engineer, an agentic framework that couples large language models (LLMs) to deterministic engineering backends in a closed loop: natural-language requirements are converted into design-domain geometry and mesh; topology is optimized with bi-directional evolutionary structural optimization (BESO) coupled to the CalculiX solver; and member sizes are refined with particle swarm optimization (PSO) coupled to Zwind under offshore aero-hydro-servo-elastic load cases. To explore many designs without per-candidate certification cost, an Automated Reviewer scores each candidate on five dimensions (capacity, steel intensity, unit cost, constructability, and fatigue life) using piecewise-linear functions calibrated on 11 real floating-wind projects. Search terminates only when a candidate reaches a composite score $S \ge 85$ (grade A) with no subscore below 60. We validated this gate by submitting the top-scoring design to the China Classification Society (CCS) for Approval in Principle (AIP), which it passed; AIP is thus an external check that the reviewer tracks professional judgment, not the daily objective. The certified design outperforms the human-optimized TuQiang baseline, reducing steel mass and unit capital cost by 8.1% each while meeting all AIP criteria. This verification-closed regime, in which every proposal is judged by deterministic physics and codified limit states, distinguishes The AI Engineer from open-ended generative systems. Remaining limits include detailed design and fabrication-hard constraints.